Vojta's abc conjecture for entire curves in toric varieties highly ramified over the boundary
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910016982745088 |
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| author | Ru, Min Wang, Julie Tzu-Yueh |
| author_facet | Ru, Min Wang, Julie Tzu-Yueh |
| contents | We prove Vojta's abc conjecture for projective space ${\Bbb P}^n({\Bbb C})$, assuming that the entire curves in ${\Bbb P}^n({\Bbb C})$ are highly ramified over the coordinate hyperplanes. This extends the results of Guo Ji and the second-named author for the case $n=2$ (see \cite{GW22}). We also explore the corresponding results for projective toric varieties. Consequently, we establish a version of Campana's orbifold conjecture for finite coverings of projective toric varieties. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_19395 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vojta's abc conjecture for entire curves in toric varieties highly ramified over the boundary Ru, Min Wang, Julie Tzu-Yueh Complex Variables Primary 30D35, Secondary 32Q45 and 32H30 We prove Vojta's abc conjecture for projective space ${\Bbb P}^n({\Bbb C})$, assuming that the entire curves in ${\Bbb P}^n({\Bbb C})$ are highly ramified over the coordinate hyperplanes. This extends the results of Guo Ji and the second-named author for the case $n=2$ (see \cite{GW22}). We also explore the corresponding results for projective toric varieties. Consequently, we establish a version of Campana's orbifold conjecture for finite coverings of projective toric varieties. |
| title | Vojta's abc conjecture for entire curves in toric varieties highly ramified over the boundary |
| topic | Complex Variables Primary 30D35, Secondary 32Q45 and 32H30 |
| url | https://arxiv.org/abs/2410.19395 |